# Trying to calculate Vae by Kirchhoff KCL

I have this circuit.

I am trying to calculate the voltage between A and E by using Kirchhoff current law.

This is what I did.

First I wrote the equation for the left side, starting at A clockwise:

$-V_{B2} - I_{1}R_{3} + I_{2}R_{3} - I_{1}R_{5} + V_{1} - I_{1}R_{1} = 0$

plugging in the value and simplifying, I get:

$17I_{1} - 10I_{2} = 8$

Now lets talk about I2. I assumed that this current was clockwise, so

$I_{2} = -2 A$

right?

Plugging in this value on the first equation I get

$I_{1} = -0.705 A$

Now I draw the 3 currents for the branches...

$i_1$ will be equal to $I_{1} = -0.705 A$ $i_2$ will be equal to $I_{2} = -2 A$

and

$i_3 = i_1 - i_2 = 1.294 A$

so, $V_{AE} = 2 + 1.294 \times 10 = 14.94 V$

I arrived at this value but B2 is killing me. I am not sure if I should add or subtract B2 to get $V_{AE}$

is that correct?

Adding it as you did is correct. B2 has a voltage drop ( in the A -> E) direction. Equivalently, Ve + 10*1.294 + 2 = Va. Your numbers also check out in Spice

• Thanks for the check. My brain was melting for a second. – SpaceDog Aug 6 '18 at 2:51